latex test

This post tests if the website display LaTeX correctly.

$$nu(mathrm{d}z) = begin{cases} frac{C}{(-z)^{1+Y}}e^{Gz}mathrm{d}z &, z<0\ frac{C}{(z)^{1+Y}}e^{-Mz}mathrm{d}z &, z > 0 , . end{cases}$$ $$- big{(} lambda + rho(x) big{)} u(t,x) + frac{partial{u}}{partial{t}}(t,x) + big{(}r - frac{sigma ^2}{2} - alpha big{)} frac{partial{u}}{partial{x}}(t,x) + frac{sigma^2}{2} frac{partial^2{u}}{partial{x}^2}(t,x) + int_mathbb{R} u(t, x+z) nu(mathrm{d}z) = 0$$

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lapply2 <- function(x, f, ...) {
  out <- vector("list", length(x))
  for (i in seq_along(x)) {
    out[[i]] <- f(x[[i]], ...)
  }
  out
}